一类具有交叉扩散的捕食模型的整体分歧  

Global Bifurcation for a Predator-prey Model with Cross-diffusion

作　　者：马晓丽[1] 

机构地区：[1]西安工业大学数理系,西安710032

出　　处：《西安工业大学学报》2010年第5期506-510,共5页Journal of Xi’an Technological University

基　　金：陕西省教育厅科学研究计划项目(09JK480);西安工业大学校长基金(XAGDXJJ0803)

摘　　要：研究了一类具有交叉扩散的捕食模型在齐次Dirichlet边界条件下正解的存在性.由极大值原理得到正解的先验估计.利用Crandall-Rabinowitz分歧理论,给出局部分歧正解的存在性,并将局部分歧延拓为整体分歧,从而得到正解存在的充分条件.结果表明,捕食者和被捕食者在一定条件下可以共存.The existence of positive solutions for a predator-prey model with cross-diffusion under homogeneous Dirichlet boundary conditions is studied.By the maximum principle,some a priori estimates are firstly obtained.Then by Crandall-Rabinowitz local bifurcation theory,positive solutions emanating from the semi-trivial solutions are derived.And resorting to the global bifurcation theory,we extend the local bifurcation solution to the global one.The results obtained show that the predator and the prey can co-exist under certain conditions.

关 键 词：捕食-食饵 交叉扩散 分歧 先验估计 

分 类 号：O175.26[理学—数学]